One of the earliest proofs can be found in Felix Hausdorff's
Grundzüge der Mengenlehre [1]} from 1914. But Hausdorff only
proved that almost all numbers are simply normal in base 2 and then
claimed it would be "evident" that the statement was true for other bases as
well. He didn't define normal numbers and gave no indication how to
prove a stronger version of his result. As we will show in this article,
Hausdorff's argument isn't hard to generalize, although the way to do it might
not be totally obvious either.
